Title page for ETD etd-07072011-231500


Type of Document Master's Thesis
Author Bandyopadhyay, Arka
Author's Email Address abandy2@lsu.edu
URN etd-07072011-231500
Title A Partial Order on Classical and Quantum States
Degree Master of Science in Systems Science (M.S.S.S.)
Department Computer Science
Advisory Committee
Advisor Name Title
Kundu, Sukhamay Committee Chair
Chen, Jianhua Committee Member
Lawson, Jimmie Committee Member
Keywords
  • Majorization
  • Partial Order
  • Bayesian
  • Closedness
Date of Defense 2011-07-06
Availability unrestricted
Abstract
In this work we extend the work done by Bob Coecke and Keye Martin in their paper “Partial Order on Classical States and Quantum States (2003)”. We review basic notions involving elementary domain theory, the set of probability measures on a finite set {a1, a2, ..., an}, which we identify with the standard (n-1)-simplex ∆n and Shannon Entropy. We consider partial orders on ∆n, which have the Entropy Reversal Property (ERP) : elements lower in the order have higher (Shannon) entropy or equivalently less information . The ERP property is important because of its applications in quantum information theory. We define a new partial order on ∆n, called Stochastic Order , using the well-known concept of majorization order and show that it has the ERP property and is also a continuous domain. In contrast, the bayesian order on ∆n defined by Coecke and Martin has the ERP property but is not continuous.
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